The conventional light conducting elements, e.g., the optical fibers, are composed of a light conducting core element having a relatively high refractive index and a covering layer having a relatively low refractive index, and in these conventional light conducting elements the rays which enter the element at its one end travels through the element while repeating total reflections at the interface of the core element and the covering layer. Either the double pot or other methods are used in covering the light conducting core element having the relatively high refractive index with the covering layer having the relatively low refractive index in making these conventional light conducting elements, with the consequence that there is a tendency to bubble taking place at the interface of the core element and the covering layer as well as the interface becoming unsmooth. And these conditions become the cause of impeding the effective conduction of light.
Again, in the case of the conventional light conducting synthetic resin elements such as described above, since the rays entering at one end of the element travels therethrough while repeating the total reflections, both lagging are set up in the phase velocities of the rays and loss of rays occur due to reflection.
As a proposal to eliminate such drawbacks, there has previously been disclosed in Japanese Patent 651,614 a glass fiber in which a gradual reduction in the refractive index takes place from the central axis to the surface of the fiber.
When a luminous flux enters one end of a light conducting fiber having a distribution of the refractive index which gradually becomes greater from the surface to the interior as disclosed in the aforesaid patent, the luminous flux, which has entered the light conducting element, travels therethrough without being reflected at the surface of the fiber. Hence, it becomes possible to reduce at the emerging end of the fiber the lagging of the phase velocity of the luminous flux, the spread of the luminous flux as well as the loss of light due to reflection. This is the same as the effects that are known as the so-called principles of the gas lens. If the refractive index in the cross-sectional plane of a fiber is so distributed as to be symmetric about the center of the fiber, the lagging of the phase velocity of the luminous flux at the emerging end of the fiber and the spread of the luminous flux can be reduced still further. Hence, this is desirable. Most preferred is the instance where the foregoing refractive index distribution is represented by a secondary curve of the form EQU n = n.sub. o (1 - ar.sup. 2) (1).
wherein r is the distance of the fiber in the radial direction from its center, n.sub. o is the refractive index at the center of the fiber, n is the refractive index at the point r, and a is a positive constant (the foregoing definitions of r, n, n.sub. o and a applying likewise hereinafter). When light having a given time interval is caused to enter one end of a fiber having this refractive index distribution, the light emerges from the other end of the fiber while retaining its given time interval without lagging of the phase velocity.
When this light conducting fiber is bent, and its radius of curvature exceeds a certain limit, the luminous flux passed through the fiber advances therethrough without reflection.
As is well known, a fiber represented by the foregoing equation (1) and whose length is t has the function of a convex lens having a focal length expressed by the equation EQU f = (n.sub. o .sqroot. 2 a sin .sqroot.2 t).sup.-.sup.1.
On the other hand, a fiber having a length t and a refractive index distribution expressed by the equation EQU n = n.sub. o (1+ ar.sup. 2) 2).
has the function of a concave lens having a focal length expressed by the equation EQU f= (n.sub. o .sqroot. 2a sink .sqroot.2a t).sup.-.sup.1.